
2001TextTNumericalMethodsComparisons
18 Aug 2018  Technique Narratives  Contributor(s): Swarn Singh
It is not always possible to solve a differential equation analytically.This material makes an effort to teach the basics of numerical methods for first order differential equations by following graphical and numerical approaches. Here we also discuss the order of accuracy of the methods and...

9001TextTSkinBurnModelNumericalMethods
18 Aug 2018  Technique Narratives  Contributor(s): Suruchi Singh
The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Here we learn to solve a heat equation numerically. It is difficult to study the behavior of temperature in problems with interfaces analytically so...

9001TextSSkinBurnModelNumericalMethods
18 Aug 2018  Technique Narratives  Contributor(s): Suruchi Singh
The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Here we learn to solve a heat equation numerically. It is difficult to study the behavior of temperature in problems with interfaces analytically so...

1067TModelingWithSigmoidCurves
18 Aug 2018  Modeling Scenarios  Contributor(s): Natali Hritonenko
The assignment considers two wellknown models of population growth, VerhulstPearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or Sshape. The assignment contains two opposite, but related tasks:...

1067SModelingWithSigmoidCurves
18 Aug 2018  Modeling Scenarios  Contributor(s): Natali Hritonenko
The assignment considers two wellknown models of population growth, VerhulstPearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or Sshape. The assignment contains two opposite, but related tasks:...

1032TDigoxinElimination
17 Aug 2018  Modeling Scenarios  Contributor(s): Therese Shelton
We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``firstorder reaction'' in the language of pharmacokinetics  the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

1032SDigoxinElimination
17 Aug 2018  Modeling Scenarios  Contributor(s): Therese Shelton
We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``firstorder reaction'' in the language of pharmacokinetics  the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

1131TCaffeineElimination
15 Aug 2018  Modeling Scenarios  Contributor(s): Therese Shelton
We model the concentration of caffeine eliminated from the human body at a rate proportional to the concentration. This is a ``firstorder reaction'' in the language of pharmacokinetics  the study of how drugs move in the body. This simple activity can be used to introduce differential...

1131SCaffeineElimination
15 Aug 2018  Modeling Scenarios  Contributor(s): Therese Shelton
We model the concentration of caffeine eliminated from the human body at a rate proportional to the concentration. This is a reaction in the language of pharmacokinetics  the study of how drugs move in the body. This simple activity can be used to introduce differential equations, and it can...

1130SAspirinAbsorption
15 Aug 2018  Modeling Scenarios  Contributor(s): Therese Shelton
We model the amount of aspirin absorbed by the human body at a constant rate. This is a ``zeroorder reaction'' in the language of pharmacokinetics  the study of how drugs move in the body. This simple activity can be used to introduce differential equations and it can be used to...

1130TAspirinAbsorption
15 Aug 2018  Modeling Scenarios  Contributor(s): Therese Shelton
We model the amount of aspirin absorbed by the human body at a constant rate. This is a ``zeroorder reaction'' in the language of pharmacokinetics  the study of how drugs move in the body. This simple activity can be used to introduce differential equations and it can be used to...

1089TSpreadOfDisease
15 Aug 2018  Modeling Scenarios  Contributor(s): Shinemin Lin
Many students fear the term “Differential Equations.” They think it is scary mathematics. In this project I want to use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel. That means even students with...

1089SSpreadOfDisease
15 Aug 2018  Modeling Scenarios  Contributor(s): Shinemin Lin
In this project we use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel.

1054TGrowthInFarmland
14 Aug 2018  Modeling Scenarios  Contributor(s): Richard Spindler
An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple ways. Different fits, modeling approaches, and...

1054SGrowthInFarmland
14 Aug 2018  Modeling Scenarios  Contributor(s): Richard Spindler
An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple ways. Different fits, modeling approaches, and...

6007SFunctionsAndDerivativesInSIRModels
12 Aug 2018  Modeling Scenarios  Contributor(s): Meredith Greer

6007TFunctionsAndDerivativesInSIRModels
12 Aug 2018  Modeling Scenarios  Contributor(s): Meredith Greer
Given a system of differential equations, how do the solution graphs compare with the graphs of the differential equations? Students tackle this question using SIR models for wellknown infectious diseases. The students view graphs both of solution curves and of the differential equations in the...

5026SEvictions
12 Aug 2018  Modeling Scenarios  Contributor(s): Mary Vanderschoot

5026TEvictions
12 Aug 2018  Modeling Scenarios  Contributor(s): Mary Vanderschoot
In this project, students develop two SIS models to study eviction trends in a population of nonhomeowner households using an actual eviction rate. (The Eviction Lab at Princeton University has developed a nationwide database of evictions based on 83 million eviction records.) As the first...

Kaabar, Mohammed2018A Friendly Introduction to Differential Equations
29 Jul 2018  Free Online Texts  Contributor(s): Mohammed K A Kaabar
In this book, there are five chapters: The Laplace Transform, Systems of Homogeneous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential Equations, and Applications of Differential Equations. In...